1. The problem asks to sort the cards into groups of equivalent expressions. 2. Let's analyze each card's expression and simplify or rewrite them to identify equivalences. Card A: $3 \times x \div 4 = \frac{3x}{4}$ Card B: $x + \frac{3}{4}$ (sum, not multiplication) Card C: $\frac{4}{3} x$ Card D: $\frac{4 \times x \times x}{3} = \frac{4x^2}{3}$ Card E: $\frac{3}{4} x x = \frac{3}{4} x^2$ Card F: $\frac{3}{4} x$ Card G: $\frac{3}{4} + x$ (sum, not multiplication) Card H: $\frac{3x}{4}$ Card I: $\frac{4x}{3}$ Card J: $3 + \frac{x}{4}$ (sum, not multiplication) 3. Grouping equivalent expressions: - Group 1 (expressions equal to $\frac{3x}{4}$): Cards A, H - Group 2 (expressions equal to $x + \frac{3}{4}$): Cards B, G - Group 3 (expressions equal to $\frac{4}{3} x$): Cards C, I - Group 4 (expressions equal to $\frac{4x^2}{3}$): Card D alone - Group 5 (expressions equal to $\frac{3}{4} x^2$): Card E alone - Group 6 (expressions equal to $\frac{3}{4} x$): Card F alone - Group 7 (expressions equal to $3 + \frac{x}{4}$): Card J alone 4. Cards D, E, F, and J are each in their own groups because their expressions are unique and not equivalent to others. Final grouping: - Group 1: A, H - Group 2: B, G - Group 3: C, I - Group 4: D - Group 5: E - Group 6: F - Group 7: J